Solve 2/3*5*5*5+7/2*5*5-15*5+4

$$\frac{ 2 }{ 3 } \times 5 \times 5 \times 5+ \frac{ 7 }{ 2 } \times 5 \times 5-15 \times 5+4$$

Evaluate

$$\frac{599}{6}\approx 99.833333333$$

Solution Steps

Express \frac{2}{3}\times 5 as a single fraction.

$$\frac{2\times 5}{3}\times 5\times 5+\frac{7}{2}\times 5\times 5-15\times 5+4$$

Multiply 2 and 5 to get 10.

$$\frac{10}{3}\times 5\times 5+\frac{7}{2}\times 5\times 5-15\times 5+4$$

Express \frac{10}{3}\times 5 as a single fraction.

$$\frac{10\times 5}{3}\times 5+\frac{7}{2}\times 5\times 5-15\times 5+4$$

Multiply 10 and 5 to get 50.

$$\frac{50}{3}\times 5+\frac{7}{2}\times 5\times 5-15\times 5+4$$

Express \frac{50}{3}\times 5 as a single fraction.

$$\frac{50\times 5}{3}+\frac{7}{2}\times 5\times 5-15\times 5+4$$

Multiply 50 and 5 to get 250.

$$\frac{250}{3}+\frac{7}{2}\times 5\times 5-15\times 5+4$$

Express \frac{7}{2}\times 5 as a single fraction.

$$\frac{250}{3}+\frac{7\times 5}{2}\times 5-15\times 5+4$$

Multiply 7 and 5 to get 35.

$$\frac{250}{3}+\frac{35}{2}\times 5-15\times 5+4$$

Express \frac{35}{2}\times 5 as a single fraction.

$$\frac{250}{3}+\frac{35\times 5}{2}-15\times 5+4$$

Multiply 35 and 5 to get 175.

$$\frac{250}{3}+\frac{175}{2}-15\times 5+4$$

Least common multiple of 3 and 2 is 6. Convert \frac{250}{3} and \frac{175}{2} to fractions with denominator 6.

$$\frac{500}{6}+\frac{525}{6}-15\times 5+4$$

Since \frac{500}{6} and \frac{525}{6} have the same denominator, add them by adding their numerators.

$$\frac{500+525}{6}-15\times 5+4$$

Add 500 and 525 to get 1025.

$$\frac{1025}{6}-15\times 5+4$$

Multiply 15 and 5 to get 75.

$$\frac{1025}{6}-75+4$$

Convert 75 to fraction \frac{450}{6}.

$$\frac{1025}{6}-\frac{450}{6}+4$$

Since \frac{1025}{6} and \frac{450}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1025-450}{6}+4$$

Subtract 450 from 1025 to get 575.

$$\frac{575}{6}+4$$

Convert 4 to fraction \frac{24}{6}.

$$\frac{575}{6}+\frac{24}{6}$$

Since \frac{575}{6} and \frac{24}{6} have the same denominator, add them by adding their numerators.

$$\frac{575+24}{6}$$

Add 575 and 24 to get 599.

$$\frac{599}{6}$$

Factor

$$\frac{599}{2 \cdot 3} = 99\frac{5}{6} = 99.83333333333333$$